Least Common Multiple (LCM) of 39 and 112
The least common multiple (LCM) of 39 and 112 is 4368.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 39 and 112?
First, calculate the GCD of 39 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 112 = 0 remainder 39 |
| 2 | 112 ÷ 39 = 2 remainder 34 |
| 3 | 39 ÷ 34 = 1 remainder 5 |
| 4 | 34 ÷ 5 = 6 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 17 | 2210 |
| 103 and 132 | 13596 |
| 101 and 172 | 17372 |
| 49 and 191 | 9359 |
| 108 and 52 | 1404 |